Delay-dependent robust control for uncertain Linear systems with distributed and multiple delays

Document Type : Research Article


1 Fasa University

2 Department of Biochemistry, University of Toronto



Time-delay in dynamical systems is often a source of instability and poor performance which presents in many applications. This paper deals with the robust control problem for class of uncertain linear neutral systems with multiple state and state derivatives delays. The parametric uncertainties are time varying and unknown but norm bounded.
In this paper by introducing a new Lyapunov functional, the stability condition is extended to structured uncertain neutral systems. so new ( Descriptor ) model transformation and a corresponding Lyapunov functional are introduced for stability analysis of systems with discrete and distributed multiple delay.
Sufficient conditions are given in terms of linear matrix inequalities ( LMI ) and refer to neutral systems with discrete and distributed delays. Based on the stability condition, designing delay dependent / independent state feedback control is formulated. Solving the LMI problems, a robust memoryless state feedback control law is designed for all admissible uncertainties. The results depend on the size and varying rate of the delays.
In this paper the presented model transformation and Lyapunov function can be applied further to H∞ control of linear uncertain systems with multiple state delays. Two examples are provided to show the effectiveness of the proposed strategy .